Question: Simplify the following expression: $z = \dfrac{-7t^2 - 42t + 189}{t - 3} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ z =\dfrac{-7(t^2 + 6t - 27)}{t - 3} $ Then we factor the remaining polynomial: $t^2 + {6}t {-27} $ ${-3} + {9} = {6}$ ${-3} \times {9} = {-27}$ $ (t {-3}) (t + {9}) $ This gives us a factored expression: $\dfrac{-7(t {-3}) (t + {9})}{t - 3}$ We can divide the numerator and denominator by $(t + 3)$ on condition that $t \neq 3$ Therefore $z = -7(t + 9); t \neq 3$